PHOENIX – Republicans are focusing on President Obama, not Gabrielle Giffords, and sensing a chance to capture the former congresswoman's seat in southern Arizona.

Voters are deciding in Tuesday's special election whether Republican Jesse Kelly, who narrowly lost to Giffords in 2010, or Democrat Ron Barber, a former Giffords aide asked by the lawmaker to pursue the seat, will complete the remainder of her term.

Giffords relinquished the seat in January to concentrate on her recovery from a gunshot wound to the head. Giffords and Barber were injured in the January 2011 shooting rampage outside a Tucson grocery store that killed six people, including a 9-year-old girl and a federal judge, and wounded 11 others.

Giffords largely has shunned public appearances in the race, but in the closing days is stepping out to help Barber. She joined the candidate at a get-out-the-vote rally Saturday.

Holding onto the seat is crucial for Democrats if they want to regain control of the House.

The party needs a net gain of 25 seats in November to grab the majority from Republicans, who now hold a 240-192 advantage with three vacancies, including Giffords' seat. Reflecting the closeness of the Arizona contest, Democrats made a last-minute appeal for money that referred to Kelly as a "radical tea party Republican" and said Barber would fight to continue Giffords' legacy in Congress.

Republicans who scoff at Democratic claims about winning the House are riding high after a decisive victory in Wisconsin's gubernatorial election last Tuesday and have set their sights on Arizona. A victory Tuesday would give party leaders a chance to claim momentum five months before November and fine-tune their plan to link Democratic candidates to Obama, the incumbent at the top of the ticket.

"Rubberstamp Ron Barber. More failed Obama policies that hurt Arizona," says the latest television ad from the National Republican Congressional Committee.

Early voting began May 17. Republican-affiliated groups have spent $1.3 million compared with $900,000 by Democratic-affiliated groups. The outside spending has helped Kelly counter Barber's fundraising edge. Barber had $390,000 cash on hand at the end of May to Kelly's $83,000.

More than 123,000 people had returned ballots they received by mail, and it's anticipated that nearly two-thirds of the votes cast will be done through early voting.

Kelly says he would seek to repeal Obama's health care overhaul law and oppose any effort to end the tax cuts enacted under President George W. Bush. Barber talks about changing some parts of the health law, requiring the wealthy to pay more to produce revenue and lowering taxes on the middle class.

Republicans seized on Barber's recent stumble. In the latest candidate debate, Barber declined to say whom he would vote for in the presidential election. Republicans said Barber couldn't be honest with voters. He campaign tried to clarify his nonanswer, saying later that he supported the president.

"That question in the debate was a diversion, an attempt to nationalize the debate," Barber told The Associated Press. "This is about southern Arizona. It's not about the president."

Democrats are trying to cast the 30-year-old Kelly as too extreme for a district that has historically supported lawmakers who reached across the aisle to forge compromise. Before Giffords, Republican Jim Kolbe represented the district for 22 years.

Democrats point to Kelly's past comments about Social Security, including his remark in the 2010 race that "you have to take steps to reform it, to privatize it, to phase it out."

A Democratic-affiliated group, the House Majority PAC, is running an ad filled with past Kelly comments. Most notably, he criticized Giffords during the 2010 campaign, saying, "and now she stands there with that smile and pretends to be some kind of hometown hero. She's a hero of nothing," he said.

The ad's narrator notes the comments were made two years ago -- months before the shooting -- but that distinction could be lost among those focused on the disdain in Kelly's voice as he speaks of Giffords. The comments came as Kelly was talking about spending policies Giffords supported that he said were bankrupting the nation.

Kelly, a 6-foot-8 Marine who served in Iraq, has shifted his position on several issues. On his campaign website, he said he would not support any overhaul of Social Security that would privatize it, cut benefits or raise the retirement age. He also has aired a television ad with his grandfather where he promises to protect Social Security and Medicare.

Kelly's campaign declined to make him available for an interview with the AP.

Barber, 66, says that future generations are financing the benefits that older people now receive.

Letting workers opt out of the program now would simply lead to the program's collapse.

"Getting people out of the program will not save it," Barber said when the two debated in late May.

Democrats argue that Barber will continue Giffords' work and hope the good will that she engendered with Arizona voters who have following her recovery will benefit him. Before serving as a Giffords aide, Barber worked with the disabled and their families at the Arizona Division of Developmental Disabilities. He and his wife also owned two children's toy and clothing stores.

Jeffrey Rogers, chairman of the Pima County Democratic Party, said he believes voters will be comforted by the mild-mannered, soft-spoken Barber. But Rogers did express surprise that Barber didn't rely on Giffords more for the campaign.

"I would have brought her in more," he said. "She's very popular."

Barber insists that his campaign has reached out to Giffords and "she has done everything we have asked her to do."

After Tuesday's election, the candidates will immediately regroup in an effort to win a full term that would begin with next year's Congress.

Most voters in the current district will become part of the newly redrawn district that becomes more Democratic, with the Republican voter-registration edge dropping from about 25,500 to about 2,000. Independents will continue to play a big factor in determining who represents the region in Congress. Registered independents make up about 31 percent of the voters in the new district.